In: Statistics and Probability
In January 2003, the FAA ordered that passengers be weighed
before boarding 10- to 19-seat passenger planes. The order was
instituted in response to a crash that occurred on January 8, 2003,
in Charlotte, North Carolina, in which all 21 passengers, including
the pilot and co-pilot,of a 19-seat Beech 1900 turboprop died. One
possible cause of the crash was that the plane may have been
carrying too much weight. The airlines were asked to weigh adult
passengers and carryon bags randomly over a one-month period to
estimate the mean weight per passenger (including luggage). A total
of 426 people and their luggage were weighed, and the sample data
are contained in a data file called FAA.
Required Task:
1. Prepare a descriptive analysis of the data using charts, graphs, and numerical measures.
Weight | Gender | Age |
197 | Male | 55 |
171 | Male | 47 |
212 | Male | 62 |
239 | Male | 49 |
237 | Male | 36 |
252 | Male | 47 |
146 | Male | 46 |
199 | Male | 47 |
235 | Male | 52 |
176 | Male | 62 |
186 | Male | 56 |
159 | Male | 51 |
155 | Male | 67 |
179 | Male | 51 |
184 | Male | 56 |
148 | Male | 44 |
190 | Male | 53 |
194 | Male | 52 |
209 | Male | 55 |
195 | Male | 50 |
196 | Male | 51 |
195 | Male | 54 |
241 | Male | 47 |
203 | Male | 59 |
200 | Male | 57 |
191 | Male | 58 |
258 | Male | 52 |
228 | Male | 57 |
269 | Male | 50 |
187 | Male | 54 |
250 | Male | 42 |
161 | Male | 53 |
220 | Male | 50 |
229 | Male | 61 |
257 | Male | 42 |
203 | Male | 53 |
191 | Male | 48 |
223 | Male | 50 |
195 | Male | 44 |
225 | Male | 53 |
166 | Male | 64 |
182 | Male | 52 |
164 | Male | 65 |
195 | Male | 47 |
204 | Male | 51 |
206 | Male | 49 |
196 | Male | 55 |
264 | Male | 47 |
158 | Male | 61 |
185 | Male | 52 |
135 | Male | 70 |
244 | Male | 52 |
170 | Male | 50 |
187 | Male | 53 |
225 | Male | 55 |
218 | Male | 58 |
229 | Male | 49 |
221 | Male | 48 |
168 | Male | 53 |
175 | Male | 68 |
224 | Male | 45 |
214 | Male | 51 |
180 | Male | 56 |
198 | Male | 56 |
209 | Male | 53 |
220 | Male | 56 |
209 | Male | 47 |
180 | Male | 56 |
256 | Male | 53 |
218 | Male | 59 |
207 | Male | 54 |
227 | Male | 58 |
228 | Male | 48 |
188 | Male | 65 |
180 | Male | 55 |
235 | Male | 44 |
173 | Male | 47 |
163 | Male | 48 |
224 | Male | 46 |
222 | Male | 47 |
265 | Male | 49 |
244 | Male | 65 |
240 | Male | 55 |
208 | Male | 43 |
205 | Male | 56 |
217 | Male | 46 |
204 | Male | 60 |
177 | Male | 49 |
157 | Male | 49 |
227 | Male | 55 |
217 | Male | 59 |
222 | Male | 40 |
211 | Male | 43 |
177 | Male | 51 |
238 | Male | 55 |
197 | Male | 73 |
182 | Male | 48 |
183 | Male | 45 |
193 | Male | 61 |
193 | Male | 49 |
191 | Male | 42 |
228 | Male | 46 |
219 | Male | 43 |
189 | Male | 61 |
240 | Male | 62 |
157 | Male | 55 |
220 | Male | 43 |
202 | Male | 66 |
206 | Male | 57 |
187 | Male | 47 |
190 | Male | 62 |
228 | Male | 50 |
227 | Male | 50 |
217 | Male | 51 |
224 | Male | 65 |
249 | Male | 46 |
213 | Male | 51 |
221 | Male | 54 |
255 | Male | 51 |
196 | Male | 49 |
233 | Male | 53 |
209 | Male | 41 |
236 | Male | 62 |
201 | Male | 53 |
184 | Male | 48 |
234 | Male | 51 |
189 | Male | 62 |
219 | Male | 38 |
220 | Male | 60 |
196 | Male | 44 |
193 | Male | 40 |
168 | Male | 55 |
259 | Male | 60 |
190 | Male | 45 |
207 | Male | 50 |
199 | Male | 55 |
282 | Male | 56 |
239 | Male | 50 |
229 | Male | 47 |
241 | Male | 52 |
210 | Male | 54 |
220 | Male | 62 |
198 | Male | 34 |
172 | Male | 49 |
239 | Male | 59 |
197 | Male | 52 |
170 | Male | 60 |
226 | Male | 53 |
226 | Male | 54 |
217 | Male | 56 |
216 | Male | 54 |
188 | Male | 47 |
225 | Male | 53 |
219 | Male | 54 |
234 | Male | 51 |
130 | Male | 56 |
218 | Male | 58 |
245 | Male | 56 |
158 | Male | 43 |
206 | Male | 55 |
242 | Male | 56 |
251 | Male | 56 |
211 | Male | 40 |
209 | Male | 38 |
255 | Male | 59 |
204 | Male | 72 |
187 | Male | 54 |
229 | Male | 44 |
205 | Male | 53 |
233 | Male | 57 |
217 | Male | 46 |
244 | Male | 42 |
202 | Male | 73 |
179 | Male | 58 |
163 | Male | 50 |
136 | Male | 59 |
208 | Male | 56 |
213 | Male | 57 |
205 | Male | 57 |
210 | Male | 54 |
212 | Male | 57 |
245 | Male | 54 |
207 | Male | 60 |
175 | Male | 48 |
167 | Male | 50 |
210 | Male | 65 |
231 | Male | 45 |
164 | Male | 44 |
189 | Male | 48 |
219 | Male | 46 |
199 | Male | 61 |
196 | Male | 54 |
201 | Male | 52 |
193 | Male | 48 |
183 | Male | 57 |
222 | Male | 61 |
207 | Male | 61 |
239 | Male | 49 |
212 | Male | 54 |
207 | Male | 59 |
211 | Male | 48 |
211 | Male | 47 |
205 | Male | 48 |
172 | Male | 53 |
211 | Male | 66 |
209 | Male | 49 |
225 | Male | 44 |
185 | Male | 51 |
222 | Male | 45 |
211 | Male | 46 |
208 | Male | 46 |
228 | Male | 51 |
254 | Male | 50 |
170 | Male | 50 |
172 | Male | 58 |
220 | Male | 60 |
237 | Male | 54 |
181 | Male | 58 |
147 | Male | 55 |
181 | Male | 43 |
210 | Male | 36 |
217 | Male | 48 |
178 | Male | 58 |
182 | Male | 56 |
217 | Male | 43 |
208 | Male | 55 |
190 | Male | 41 |
208 | Male | 60 |
180 | Male | 60 |
181 | Male | 53 |
233 | Male | 55 |
249 | Male | 59 |
187 | Male | 49 |
200 | Male | 47 |
208 | Male | 51 |
255 | Male | 61 |
221 | Male | 52 |
250 | Male | 56 |
210 | Male | 40 |
247 | Male | 58 |
188 | Male | 48 |
179 | Male | 67 |
237 | Male | 47 |
230 | Male | 49 |
158 | Male | 64 |
239 | Male | 57 |
200 | Male | 53 |
174 | Male | 49 |
154 | Male | 35 |
183 | Male | 45 |
218 | Male | 57 |
230 | Male | 65 |
203 | Male | 53 |
204 | Male | 46 |
211 | Male | 60 |
195 | Male | 50 |
230 | Male | 48 |
192 | Male | 49 |
268 | Male | 60 |
225 | Male | 37 |
221 | Male | 61 |
179 | Male | 47 |
229 | Male | 45 |
244 | Male | 48 |
185 | Male | 58 |
197 | Male | 65 |
169 | Male | 55 |
242 | Male | 38 |
233 | Male | 63 |
210 | Male | 39 |
146 | Male | 49 |
219 | Male | 65 |
219 | Male | 54 |
238 | Male | 44 |
179 | Male | 52 |
238 | Male | 68 |
190 | Male | 48 |
185 | Male | 60 |
158 | Male | 41 |
242 | Male | 48 |
179 | Male | 50 |
247 | Male | 46 |
173 | Male | 52 |
194 | Male | 62 |
170 | Male | 40 |
248 | Male | 34 |
206 | Male | 56 |
214 | Male | 44 |
231 | Male | 55 |
258 | Male | 46 |
203 | Male | 59 |
177 | Male | 47 |
190 | Male | 47 |
228 | Male | 44 |
229 | Male | 44 |
219 | Male | 59 |
165 | Male | 62 |
167 | Male | 51 |
201 | Male | 56 |
188 | Male | 53 |
188 | Male | 53 |
229 | Male | 43 |
182 | Male | 59 |
202 | Male | 57 |
199 | Male | 59 |
246 | Male | 56 |
169 | Male | 49 |
180 | Male | 50 |
200 | Male | 54 |
176 | Male | 43 |
166 | Male | 53 |
147 | Male | 35 |
221 | Male | 46 |
196 | Male | 59 |
216 | Male | 44 |
150 | Male | 48 |
237 | Male | 47 |
152 | Male | 59 |
191 | Male | 45 |
179 | Male | 49 |
202 | Male | 49 |
209 | Male | 46 |
252 | Male | 52 |
191 | Male | 53 |
184 | Male | 27 |
185 | Male | 33 |
221 | Male | 51 |
240 | Male | 35 |
166 | Male | 33 |
231 | Male | 46 |
248 | Male | 30 |
187 | Male | 38 |
207 | Male | 40 |
183 | Male | 45 |
224 | Male | 46 |
211 | Male | 42 |
206 | Male | 54 |
177 | Male | 52 |
197 | Male | 29 |
225 | Male | 35 |
205 | Male | 45 |
232 | Male | 30 |
178 | Male | 27 |
225 | Male | 41 |
239 | Male | 28 |
146 | Female | 47 |
131 | Female | 45 |
139 | Female | 37 |
152 | Female | 45 |
139 | Female | 42 |
117 | Female | 37 |
123 | Female | 31 |
138 | Female | 36 |
109 | Female | 36 |
128 | Female | 35 |
123 | Female | 47 |
121 | Female | 32 |
171 | Female | 37 |
127 | Female | 48 |
96 | Female | 36 |
139 | Female | 37 |
130 | Female | 45 |
127 | Female | 28 |
160 | Female | 45 |
152 | Female | 48 |
164 | Female | 29 |
90 | Female | 39 |
107 | Female | 32 |
134 | Female | 27 |
108 | Female | 36 |
110 | Female | 33 |
114 | Female | 48 |
143 | Female | 31 |
168 | Female | 36 |
140 | Female | 43 |
135 | Female | 40 |
148 | Female | 43 |
160 | Female | 44 |
102 | Female | 37 |
154 | Female | 37 |
128 | Female | 37 |
144 | Female | 44 |
145 | Female | 36 |
120 | Female | 24 |
159 | Female | 47 |
135 | Female | 43 |
127 | Female | 55 |
136 | Female | 46 |
147 | Female | 41 |
157 | Female | 58 |
112 | Female | 57 |
133 | Female | 47 |
103 | Female | 43 |
156 | Female | 45 |
122 | Female | 52 |
159 | Female | 47 |
108 | Female | 73 |
171 | Female | 50 |
122 | Female | 55 |
163 | Female | 47 |
148 | Female | 53 |
159 | Female | 48 |
127 | Female | 50 |
132 | Female | 53 |
136 | Female | 55 |
123 | Female | 62 |
135 | Female | 55 |
128 | Female | 50 |
142 | Female | 60 |
116 | Female | 48 |
113 | Female | 48 |
124 | Female | 55 |
122 | Female | 48 |
155 | Female | 57 |
149 | Female | 49 |
113 | Female | 52 |
139 | Female | 59 |
182 | Female | 44 |
137 | Female | 70 |
115 | Female | 61 |
115 | Female | 58 |
152 | Female | 48 |
116 | Female | 58 |
93 | Female | 51 |
140 | Female | 49 |
103 | Female | 54 |
Solution: 1. Prepare a descriptive analysis of the data using charts, graphs, and numerical measures.
Answer: Let's analyze the weight variable first:
We can use excel to find the summary statistics of the weight variable. The excel output is given below:
From the excel output, we see the mean weight of 426 passenger's is with standard deviation of . The minimum weight is 90 and the maximum weight is 282. Also the skewness of the given data suggest us that weight of 426 passenger's is negatively skewed.
Since the given data is continuous, therefore it would be better to create the histogram for the given data. The histogram is given below:
Now, lets analyze the Age variable. The excel output of summary statistics is given below:
From the excel output, we see the mean age of 426 passenger's is with standard deviation of . The minimum age is 24 and the maximum age is 73. Also the skewness of the given data suggest us that age of 426 passenger's is approximately symmetric.
We can plot the histogram for the Age variable:
Now, let's explore the gender variable.
We see there are 345 males in the given data and there are 81 females in the data. We can use pie chart to graphically present the Gender variable. The Pie chart is given below: